The quantum properties of matter and radiation can be leveraged to surpass classical limits of sensing and detection. Quantum optics does so by creating and measuring nonclassical light. However, better performance requires higher photon-number states, which are challenging to generate and detect. Here, we combine photons and free electrons to solve the problem of generating and detecting high-number states well beyond those reachable with light alone and further show that an unprecedented level of sensitivity and resolution is gained based on the measurement of free-electron currents after suitably designed electron-light interactions. Our enabling ingredient is the strong electron-light coupling produced by aloof electron reflection on an optical waveguide, leading to the emission or absorption of a high number of guided photons by every single electron. We establish through rigorous theory that, by combining electron-beam splitters with two electron-waveguide interactions, the sensitivity to detect optical-phase changes can be enhanced dramatically using currently attainable technology. These results inaugurate a disruptive quantum technology relying on free electrons and their strong interaction with waveguided light.
The quantum properties of matter and radiation can be leveraged to surpass classical limits of sensing and detection. Quantum optics does so by creating and measuring nonclassical light. However, better performance requires higher photon-number states, which are challenging to generate and detect. Here, we combine photons and free electrons to solve the problem of generating and detecting high-number states well beyond those reachable with light alone and further show that an unprecedented level of sensitivity and resolution is gained based on the measurement of free-electron currents after suitably designed electron-light interactions. Our enabling ingredient is the strong electron-light coupling produced by aloof electron reflection on an optical waveguide, leading to the emission or absorption of a high number of guided photons by every single electron. We establish through rigorous theory that, by combining electron-beam splitters with two electron-waveguide interactions, the sensitivity to detect optical-phase changes can be enhanced dramatically using currently attainable technology. These results inaugurate a disruptive quantum technology relying on free electrons and their strong interaction with waveguided light.
Strong coupling in light-matter systems is a central concept in cavity quantum electrodynamics and is essential for many quantum technologies. Especially in the optical range, full control of highly connected multi-qubit systems necessitates quantum coherent probes with nanometric spatial resolution, which are currently inaccessible. Here, we propose the use of free electrons as high-resolution quantum sensors for strongly coupled light-matter systems. Shaping the free-electron wave packet enables the measurement of the quantum state of the entire hybrid systems. We specifically show how quantum interference of the free-electron wave packet gives rise to a quantum-enhanced sensing protocol for the position and dipole orientation of a subnanometer emitter inside a cavity. Our results showcase the great versatility and applicability of quantum interactions between free electrons and strongly coupled cavities, relying on the unique properties of free electrons as strongly interacting flying qubits with miniscule dimensions.
Since the birth of quantum optics, the measurement of quantum states of nonclassical light has been of tremendous importance for advancement in the field. To date, conventional detectors such as photomultipliers, avalanche photodiodes, and superconducting nanowires, all rely at their core on linear excitation of bound electrons with light, posing fundamental restrictions on the detection. In contrast, the interaction of free electrons with light in the context of quantum optics is highly nonlinear and offers exciting possibilities. The first experiments that promoted this direction appeared over the past decade as part of photon-induced nearfield electron microscopy (PINEM), wherein free electrons are capable of high-order multi-photon absorption and emission. Here we propose using free electrons for quantum-optical detection of the complete quantum state of light. We show how the precise control of the electron before and after its interaction with quantum light enables to extract the photon statistics and implement full quantum state tomography using PINEM. This technique can reach sub-attosecond time resolutions, measure temporal coherence of any degree (e.g., g(1), g(2)), and simultaneously detect large numbers of photons with each electron. Importantly, the interaction of the electron with light is non-destructive, thereby leaving the photonic state (modified by the interaction) intact, which is conceptually different from conventional detectors. By using a pulse of multiple electrons, we envision how PINEM quantum detectors could achieve a single-shot measurement of the complete state of quantum light, even for non-reproducible emission events. Altogether, our work paves the way to novel kinds of photodetectors that utilize the ultrafast duration, high nonlinearity, and non-destructive nature of electron-light interactions.
Electron beams are a formidable tool for probing nanophotonic systems [1]. Combining electron microscopy with external optical excitation in ultrafast transmission electron microscopes has enabled the mapping of optical near-fields [2] and the bunching of electrons in attosecond pulses [3, 4]. These developments are based on the stimulated inelastic scattering between electrons and light [5, 6], in which the electrons gain energy from or lose energy to the optical field. Recently, the underlying interaction strength of this process has been increased significantly by harnessing resonant enhancement of the optical field and velocity phase matching [7]. Such an increased interaction strength also benefits the spontaneous scattering of electrons with light, thus promising applications like generating complex quantum states of light [8]. In this presentation, we discuss a set of experiments on free electron quantum optics that investigate single-electron-single-photon interactions and probe the resulting entanglement. Specifically, we consider scenarios in which optical waveguide structures are placed inside a transmission electron microscope (TEM) facilitating the interaction. Electrons passing by, for example, an integrated photonic structure (cf. Fig. 1a) can inelastically scatter with the optical mode, leading to the emergence of electron-photon pair states [9]. The resulting correlation between energy-loss electrons and photons, illustrated in Fig. 1b, can be probed employing time- and energy-resolved detection of both particles, revealing a pronounced coincidence peak between their arrival times, schematically shown in Fig. 1c. Extending the photon detection setup by a second detector to allow for Hanbury Brown and Twiss (HBT) measurements, the photon statistics heralded by such energy-loss electrons can be studied [10]. The observed anti-bunching behavior indicates a nonclassical optical state with single-photon properties. The inelastic electron-light scattering underlying the electron-photon pair generation is further expected to induce entanglement in the particle energies [11], however, direct observation of quantum entanglement would be exceedingly difficult given the large number of independent quantum states available in these degrees of freedom. Therefore, we propose experiments based on the quantum eraser scheme to demonstrate this free-electron-photon entanglement in different degrees of freedom [12,13]. Specifically, we consider a double-slit geometry coherently illuminated by an electron beam such that an interference pattern can be observed on a distant screen (cf. Fig. 2a). If electrons passing through the left or right (denoted |Land |R, respectively) slit generate distinct marker photons with vertical (|V)or horizontal (|H) polarization, this interference pattern would disappear due to the entanglement of electron path and photon polarisation (cf. Fig. 2b). However, if this which-path information carried by the marker photon is erased, e.g. by mixing the polarisation states, the interference pattern can be recovered when detecting electrons and photons in coincidence. We describe an extension of this idea to an entanglement test, before discussing possible realistic implementations and presenting preliminary results on several experimental key aspects. In summary, we discuss the inelastic electron-light scattering at integrated photonic structures with applications ranging from coherent electron beam modulation using continuous-wave optical fields to the electron-driven generation of quantum optical states of light. Delving deeper into single electron-single photon interactions, we outline feasible experiments to generate and verify electron-photon entanglement with a potential extension to electron pairs based on entanglement swapping. All this adds to the toolbox of free electron quantum optics, potentially enabling novel sources of quantum light as well as quantum-enhanced sensing in electron microscopy. Generation of correlated electron-photon pairs. (a) Electrons pass over a photonic integrated circuit placed in the sample plane of a TEM, generating photons in the optical waveguides via inelastic scattering. Energy-loss electrons are detected and time-tagged behind an imaging spectrometer in coincidence with photons exiting the waveguide. (b) Inelastic scattering links the electron energy loss (green, right ladder) to the generation of photons (red, left ladder), creating correlations in energy and time. (c) A strong temporal correlation between the loss electrons and detected photons, indicated by the red dot, is observed relative to the uncorrelated zero-loss background electrons (blue line). Free-electron-photon quantum eraser. (a) Coherent electron illumination of a double-slit structure results in interference between the two pathways |Land |R.(b) If the electrons generate distinguishable marker photons, e.g. of orthogonal polarizations |Vand |H, no interference pattern can be observed due to the electron-photon entanglement. (c) Collecting these marker photons and erasing the which-path information, e.g. using a half-wave plate (λ/2), the electron interference can be recovered using electron-photon coincidence detection with single-photon detectors (SPDs) placed behind a polarizing beam splitter (PBS).
A central challenge in the emerging field of free-electron quantum optics is to achieve strong quantum interaction and single-photon nonlinearity between a flying free electron and a photonic mode. Existing schemes are intrinsically limited by electron diffraction, which puts an upper bound on the interaction length and, therefore, on the strength of quantum coupling and nonlinearity. Here, we propose “free-electron fibers”: effectively one-dimensional photonic systems where free electrons copropagate with two guided modes. The first mode applies a ponderomotive trap to the free electron, removing the limitations due to electron diffraction. The second mode strongly couples to the guided free electron with an enhanced coupling that is orders of magnitude larger than previous designs. The extended interaction lengths enabled by our scheme allow for strong single-photon nonlinearities mediated by free electrons. We predict novel quantum effects in our system such as deterministic single-photon emission and nonlinear multimode dynamics. Our proposal paves the way toward the realization of heralded macroscopic nonclassical light generation, deterministic single-photon sources, and quantum gates controlled by free-electron–photon interactions.
One of the astounding consequences of quantum mechanics is that it allows the detection of a target using an incident probe, with only a low probability of interaction of the probe and the target. This 'quantum weirdness' could be applied in the field of electron microscopy to generate images of beam-sensitive specimens with substantially reduced damage to the specimen. A reduction of beam-induced damage to specimens is especially of great importance if it can enable imaging of biological specimens with atomic resolution. Following a recent suggestion that interaction-free measurements are possible with electrons, we now analyze the difficulties of actually building an atomic resolution interaction-free electron microscope, or "quantum electron microscope". A quantum electron microscope would require a number of unique components not found in conventional transmission electron microscopes. These components include a coherent electron beam-splitter or two-state-coupler, and a resonator structure to allow each electron to interrogate the specimen multiple times, thus supporting high success probabilities for interaction-free detection of the specimen. Different system designs are presented here, which are based on four different choices of two-state-couplers: a thin crystal, a grating mirror, a standing light wave and an electro-dynamical pseudopotential. Challenges for the detailed electron optical design are identified as future directions for development. While it is concluded that it should be possible to build an atomic resolution quantum electron microscope, we have also identified a number of hurdles to the development of such a microscope and further theoretical investigations that will be required to enable a complete interpretation of the images produced by such a microscope.
Abstract Free electrons are a universal source of electromagnetic fields, and fundamentally their quantized energy exchange may facilitate generating tunable quantum light. Because the quantum features of the emitted radiation are encoded in the joint electronic and photonic state, they can only be revealed by a measurement accessing both subsystems. Here we demonstrate the coherent parametric generation of such non-classical states of light by free electrons. Investigating electron–photon correlations, we show that the quantized electron energy loss heralds the number of photons generated in a dielectric waveguide. In Hanbury Brown–Twiss measurements, we observe an electron-heralded single-photon state using antibunching intensity correlation, whereas two-quantum energy losses of individual electrons yield pronounced two-photon coincidences. Our results will enable the tailored preparation of higher-number Fock and other optical quantum states on the basis of controlled interactions with free-electron beams.